How to calculate the theoretical capacity of battery electrode materials
The theoretical capacity of a battery electrode material can be estimated using the relation:
$\frac{xF}{M}$where F is the Faraday constant, x is the number of faradays involved in the reaction, and M is the molar mass of the material.
Hence, according to Eq.1, the theoretical charge or discharge capacity of LiCoO_{2} can be calculated to be 274 mAh/g, using 1.0, 26.80 Ah/mol, and 97.87 g/mol for x, F and M, respectively.
$LiCo{O}_{2}\leftrightarrow L{i}_{\mathit{1}\mathit{\u2013}x}Co{O}_{2}+x{\mathrm{Li}}^{+}+x{\mathrm{e}}^{\u2013}...............................\left(1\right)$Likewise, according to Eq.2, the theoretical charge or discharge capacity of graphite (C) can be calculated to be 372 mAh/g, using 1/6, 26.80 Ah/mol, and 12 g/mol for x, F and M, respectively.
$C\mathit{}+\mathit{}xL{i}^{\mathit{+}}\mathit{}+\mathit{}x{e}^{\mathit{\u2013}}\mathit{}\mathit{\leftrightarrow}\mathit{}L{i}_{x}C\mathit{}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{.}\mathit{\left(}\mathit{2}\mathit{\right)}$
Examples are shown in the table below.
Anode | Cathode | x/ mol | Thoeretical Capacity/ mAh g^{-1} | Attainable Capacity/ mAh g^{-1} | |
Graphite | ♦ | 1/6 | 372 | 350 | |
Li_{4}Ti_{5}O_{12} | ♦ | 3 | 175 | 170 | |
Si | ♦ | 3.75 | 3579 | same | |
LiCoO_{2} | ♦ | 1 | 274 | 145 | |
LiNi_{1/3}Co_{1/3}Mn_{1/3}O_{2} | ♦ | 1 | 278 | 150 | |
LiFePO_{4} | ♦ | 1 | 170 | 160 |